Geometric Homology

The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately addressed. In particular, our goal is to construct a chain level t...

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Bibliographic Details
Published in:arXiv.org 2014-09
Main Author: Lipyanskiy, Max
Format: Article
Language:English
Subjects:
Corners
Homology
Intersections
Online Access:Get full text
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Summary:The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately addressed. In particular, our goal is to construct a chain level theory based on smooth mappings of manifolds with corners. In addition, we will avoid using the fact that smooth manifolds with can be triangulated. As we shall see, transversality and intersections play a major role in setting up this theory. From a pedagogical viewpoint, having intersection theory arguments available from the start facilitates simple and intuitive computations.
ISSN:2331-8422